Solve 54/360*8^2*pi-54/360*5^2pi

$$\frac { 54 } { 360 } \cdot 8 ^ { 2 } \cdot \pi - \frac { 54 } { 360 } \cdot 5 ^ { 2 } \pi$$

Evaluate

$$\frac{117\pi }{20}\approx 18.378317024$$

Solution Steps

Reduce the fraction \frac{54}{360} to lowest terms by extracting and canceling out 18.

$$\frac{3}{20}\times 8^{2}\pi -\frac{54}{360}\times 5^{2}\pi$$

Calculate 8 to the power of 2 and get 64.

$$\frac{3}{20}\times 64\pi -\frac{54}{360}\times 5^{2}\pi$$

Express \frac{3}{20}\times 64 as a single fraction.

$$\frac{3\times 64}{20}\pi -\frac{54}{360}\times 5^{2}\pi$$

Multiply 3 and 64 to get 192.

$$\frac{192}{20}\pi -\frac{54}{360}\times 5^{2}\pi$$

Reduce the fraction \frac{192}{20} to lowest terms by extracting and canceling out 4.

$$\frac{48}{5}\pi -\frac{54}{360}\times 5^{2}\pi$$

Reduce the fraction \frac{54}{360} to lowest terms by extracting and canceling out 18.

$$\frac{48}{5}\pi -\frac{3}{20}\times 5^{2}\pi$$

Calculate 5 to the power of 2 and get 25.

$$\frac{48}{5}\pi -\frac{3}{20}\times 25\pi$$

Express \frac{3}{20}\times 25 as a single fraction.

$$\frac{48}{5}\pi -\frac{3\times 25}{20}\pi$$

Multiply 3 and 25 to get 75.

$$\frac{48}{5}\pi -\frac{75}{20}\pi$$

Reduce the fraction \frac{75}{20} to lowest terms by extracting and canceling out 5.

$$\frac{48}{5}\pi -\frac{15}{4}\pi$$

Combine \frac{48}{5}\pi and -\frac{15}{4}\pi to get \frac{117}{20}\pi .

$$\frac{117}{20}\pi$$